Full length article: Asymptotic properties of extremal polynomials corresponding to measures supported on analytic regions

Authors:
Brian Simanek
Affiliations:
-
Venue:
Journal of Approximation Theory
Year:
2013

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Abstract

Let G be a bounded region with simply connected closure G@? and analytic boundary and let @m be a positive measure carried by G@? together with finitely many pure points outside G. We provide estimates on the norms of the monic polynomials of minimal norm in the space L^q(@m) for q0. In case the norms converge to 0, we provide estimates on the rate of convergence, generalizing several previous results. Our most powerful result concerns measures @m that are perturbations of measures that are absolutely continuous with respect to the push-forward of a product measure near the boundary of the unit disk. Our results and methods also yield information about the strong asymptotics of the extremal polynomials and some information concerning Christoffel functions.